Caustics caused by vortices on active and inactive particles

Small and heavy particles or droplets in vortical flows are centrifuged out of regions of high vorticity and form caustics, at intermediate Stokes number [Ravichandran and Govindarajan, Physics of Fluids 27, 033305 (2015)]. For a dilute suspension of non-interacting particles, if the particle velocity field can indeed be written down, caustics mark the divergence in the gradient of this field. Here we observe singular features in particle number-density. These singularities represent interparticle collisions which are consequential in coalescence and aggregation processes [Wilkinson et al. Phys. Rev. Lett. 97, 048501 (2006)]. 

In the limit of vanishing Stokes number, we find that the flow regions promoting caustics of finitely dense particles have significantly different characteristics from those of infinitely dense particles. This is exemplified in 2D where there is an upper limit on the background strain only for finitely dense particles. We study the motion of inertialess motile particles in ambient flows and show that these dynamics can be mapped to that of inertial non-motile particles. Using a singular perturbation analysis we show that self propelled particles display “active” caustics in the inner region of the vortex flow, and we numerically study the dynamic identification of caustics regions in turbulent flows based on the Okubo Weiss parameter and finite time Lyapunov exponents. Finally, we discuss how caustics limit the applicability of a continuum description of particles.